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<div><a href="../../index.html">Home</a> &gt;  <a href="#">tt2</a> &gt; <a href="index.html">exp</a> &gt; fclencurt.m</div>

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<h1>fclencurt
</h1>

<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="box"><strong>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</strong></div>

<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="box"><strong>function [x,w]=fclencurt(N1,a,b) </strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="fragment"><pre class="comment">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 fclencurt.m - Fast Clenshaw Curtis Quadrature

 Compute the N nodes and weights for Clenshaw-Curtis
 Quadrature on the interval [a,b]. Unlike Gauss 
 quadratures, Clenshaw-Curtis is only exact for 
 polynomials up to order N, however, using the FFT
 algorithm, the weights and nodes are computed in linear
 time. This script will calculate for N=2^20+1 (1048577
 points) in about 5 seconds on a normal laptop computer.

 Written by: Greg von Winckel - 02/12/2005
 Contact: gregvw(at)chtm(dot)unm(dot)edu

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</pre></div>

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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../../matlabicon.gif)">
</ul>
This function is called by:
<ul style="list-style-image:url(../../matlabicon.gif)">
</ul>
<!-- crossreference -->



<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../../up.png"></a></h2>
<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function [x,w]=fclencurt(N1,a,b)</a>
0002 
0003 <span class="comment">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</span>
0004 <span class="comment">%</span>
0005 <span class="comment">% fclencurt.m - Fast Clenshaw Curtis Quadrature</span>
0006 <span class="comment">%</span>
0007 <span class="comment">% Compute the N nodes and weights for Clenshaw-Curtis</span>
0008 <span class="comment">% Quadrature on the interval [a,b]. Unlike Gauss</span>
0009 <span class="comment">% quadratures, Clenshaw-Curtis is only exact for</span>
0010 <span class="comment">% polynomials up to order N, however, using the FFT</span>
0011 <span class="comment">% algorithm, the weights and nodes are computed in linear</span>
0012 <span class="comment">% time. This script will calculate for N=2^20+1 (1048577</span>
0013 <span class="comment">% points) in about 5 seconds on a normal laptop computer.</span>
0014 <span class="comment">%</span>
0015 <span class="comment">% Written by: Greg von Winckel - 02/12/2005</span>
0016 <span class="comment">% Contact: gregvw(at)chtm(dot)unm(dot)edu</span>
0017 <span class="comment">%</span>
0018 <span class="comment">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</span>
0019 
0020 N=N1-1; bma=b-a;
0021 c=zeros(N1,2);
0022 c(1:2:N1,1)=(2./[1 1-(2:2:N).^2 ])'; c(2,2)=1;
0023 f=real(ifft([c(1:N1,:);c(N:-1:2,:)]));
0024 w=bma*([f(1,1); 2*f(2:N,1); f(N1,1)])/2;
0025 x=0.5*((b+a)+N*bma*f(1:N1,2));</pre></div>
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